Construction and analysis of multi-lump solutions of dispersive long wave equations via integer partitions

2024/10/26 by An, Yong-Ning, Guo, Rui
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2410.20059

Abstract

In this paper, the relation between the integer partition theory and a kind of rational solution of the dispersion long wave equations is studied. For the integer partition λ= (λ1,λ2,... ,λn) of positive integer N, with the degree vector m = (m1,m2,... ,mn), the corresponding M lump solution can be obtained where M = N + n mn. Combined with the generalized Schur polynomial and heat polynomial, the asymptotic positions of peaks are studied, and the arrangement of multi-peak groups in multi-lump solutions are obtained, as well as the relationship between the patterns formed by single-peak groups and the corresponding integer partition.

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